You may think that a resistor is always a resistor and nothing more. Think again friends. When the frequency gets high and especially when it gets very high resistor values change and can also be inductive or capacitive.
This page gives data on a wide range of resistor values for a wide range of frequencies. Data is also included for carbon composition and carbon film resistors. Upon looking at the tables your first thought is likely to be TMI (too much information). On the page with each table I will discuss the meaning of each column and what is most important. For those who just can't wait here are the links to the charts.
Carbon Composition Resistors.
1/4 Watt Carbon Film.
1/2 Watt Carbon Film.
1 Watt Carbon Film.
Selecting Resistor Values and Frequencies.When ever data are to be collected over a wide range of values, several decades, a geometric progression of values is better than an arithmetic progression. I found this out the hard way in my first electronics lab where I had to plot a frequency response from 100 Cycles, as they were known then, to 1 megacycle. When I sat down with the sheet of semi log paper to plot it the points at the high end were so close together that they could hardly be resolved on the graph.Just to clarify here is an example of an arithmetic series.
2 4 6 8 10 12 etc.
Here is an example of a geometric series.
2 4 8 16 32 64 etc.
The frequency range was set by the Boonton model 250A RX Meter used to make the measurements. The range I selected was from 0.5 to 200 MHz. Note: The instrument goes up to 250 MHz but it is probably 50 years old if it's a day. 200 MHz is about its practical upper limit of usefulness. I wanted a total of 10 data points. The formula that gives the factor that relates the n+1 term to the nth term is,
Factor = (H/L)(1/(N-1))
Where L is the lowest frequency point, H is the highest frequency point, and N is the number of points, 10 in this case. I enter the first frequency, 0.5 MHz into cell A5 of the spread sheet and programmed the formula into cell A6. When the formula in cell A6 is copied and pasted into Cell A7 the reference is changed to A6 so it just keeps multiplying the factor by the previous frequency to obtain the next frequency.
Resistor values are not so cut and dried because they only are available in specific values. If you wanted to go from 10 ohms to 10 megohms with 13 points you would get,
Factor = (10E7/10)^(1/12) = 3.162.
Which means that the first value would be 10 ohms and the second 31.62 ohms. The next one after that would be 100 ohms. One problem. They don't make a 31.62 ohm resistor. How about a 33 ohm? Close enough. So we will use 10 ohm, 33 ohm, 100 ohm, 330 ohm, 1 k ohm, 3.3 k ohm, 10 k ohm, 33 k ohm, 100 k ohm, 330 k ohm, 1 megohm, 3.3 megohm, and 10 megohm.
One minor problem. The resistance dial on the RX Meter only goes down to 15 ohms. Alright, we'll begin with 15 ohms. Another small problem. When a 15 ohm resistor was measured with the instrument the capacitance dial went off scale. See under the heading, "The Boonton 250A RX Meter" below. Alright, we'll try a 22 ohm. Fine but now the next jump is kind of short from 22 to 33 ohms. 47 ohms is a good next value so we'll go with that. That's close enough to 50 ohms to be of interest to RF engineers so it's a good choice. From 100 ohms on up the 100 330 etc progression will be followed.
The problem with going all the way to 10 megohms is the resistance dial on the 250A.
As you can see there are no interpolation marks between 100 k ohms and infinity. Also there aren't any marks between 50 k and 100 k. The mark between 30 k and 40 k is 35 k which reveals the nonlinearity of the scale which further complicates interpolation. The mark below 30 k is 28 k and the one below that, 26 k. So we will lose all resistor values above 100 k ohm. You may be wondering why deal with 100 k since the scale can not give meaningful values. At VHF the value of the 100 k ohm resistor falls to values where the scale can give meaningful values. The 4 values above 100 k were tested for capacitance and gave nearly constant values ranging from 0.3 to 0.6 pf that were different for each type of resistor. Now with resistor and frequency values set the testing began.
The Boonton 250A RX Meter.
To call this instrument a meter is a complete misnomer. It is a bridge which must be manually balanced as electrical measurement bridges have had to be for more than 100 years.
It is a rather unique bridge because it reads the parallel combination of resistance and capacitance. The resistance range is from 15 ohms to infinity. The capacitance range is from 20 pf to -100 pf. Negative capacitance? Yes!
As you turn the dial it goes from positive 20 pf down to zero and then to negative 100 pf. Negative capacitance is really inductance. It is the value of capacitance that will tune the effective inductance to parallel resonance at the frequency that has been set on the Frequency Dial. Think of it. They couldn't have done it any other way. Once in the inductive part of the range the inductance value would be different for every frequency.
This bridge seems to have been designed for exactly what I am using it for in this research project. I am very well acquainted with it because each of my two previous employers had one. They were the astronomy department of the University of Florida and the physics and astronomy department of Western Kentucky University. Both universities had radio astronomy divisions and it was thought that the RX bridge would be useful for antenna work. However the capacitance range is too limited for that purpose. A slightly off-tuned antenna will place it's impedance off the end of the capacitance scale. Also the resistance scale is much wider than an antenna engineer would ever need. Although it was a bad choice for antenna work it was very useful for small discrete networks and with the transistor test jig, invaluable for determining the RF characteristics of transistors.
If I recall correctly this instrument cost in the neighborhood of 2,000 dollars in the 1960s. That was a lot more money then than it is now. You could buy a pretty good car for 4,000 dollars. I bought it off eBay for a song and it needed some work. It seems to be in pretty good condition considering all it's been through. It was a quality instrument and the fact that it still works and is stable speaks to that.
Verification of Instrument Accuracy.First I did the easiest thing to do which was to check the frequency accuracy. Connecting a frequency counter to the bridge terminals provided enough signal to the counter. While I didn't check every dial marking on every band I check points near each end of each band and approximately in the center. Every frequency was within, or just a smidgen outside of 1%. (That's a technical term).
Next I attempted to verify the capacitance scale. Because the scale only goes to 20 pf capacitive I couldn't use a very large capacitor. I got out an 18 pf capacitor and it measured 18.1 pf on the HP 4261A RLC meter. On the 250A it read 17.5 at 0.5 and 5 MHz. It read 19 pf at 50 MHz. I have no way of knowing if this change is caused by the capacitor or the bridge. Verifying the scale in the negative direction required an inductor. I used a 2.5 mH choke which measured 2.51 mH on the 4261A. Calculations gave a resonating capacitance of 40.37 pf at 0.5 MHz. When measured on the 250A the reading was -37.4 pf. Considering that the calculations do not account for the parasitic capacitance of the choke I think that's pretty good. No attempt was made to go higher in frequency. The 4261A measures capacitance and inductance at 1 kHz and the drastic frequency difference is likely to make such measurements meaningless. I'm sure there are standard capacitors and resistors that have well known characteristics at various frequencies but I don't have any. I can imagine how expensive they must be and so I doubt I will ever have any.
Measurement Procedure.First each resistor was measured using the 4261A LCR meter.
The picture shows a 22 ohm resistor connected directly to the measurement terminals of the meter. The display is showing 21.9 ohms. I suspect that this is a self balancing analog bridge with digital readouts. Note that the frequency is set to 120 Hz to be sure the measurement is as close as possible to the true DC resistance.
The 250A procedure is rather involved. It is described here to let you know how much time this project required. After the frequency is set the detector must be tuned for maximum meter indication with the dials set to guarantee a strong signal to the null detector. After the detector has been peaked the dials are set to 0 capacitance and infinity on the resistance dial. Then the zero balance controls are adjusted for minimum meter deflection. This process must be repeated each time the frequency is changed.
The resistor under test is then connected to the terminals and the dials adjusted for minimum meter deflection. The dials are read and the data recorded in the spread sheet. Once the frequency was set up all resistors were measured before changing frequency.
Unfortunately I don't have any dog bone resistors. I would be curious to know how they compare to carbon composition and carbon film. If anyone has a collection and would like to loan me 9 of them in the values used in this experiment please contact me. There is an email link on the home page of this site.
Here are the links again.
Carbon Composition Resistors.
1/4 Watt Carbon Film.
1/2 Watt Carbon Film.
1 Watt Carbon Film.
Download the spreadsheet.